Question:
Sex ratio at birth is biased towards females in a mongoose population. If the probability of having a daughter is 0.7 in this population, and if sex determination of each offspring is an independent event, then the probability that a female with a litter of four offspring has at least one son is \(\underline{\hspace{0cm}}\) (Round off to two decimal places.)
Sex ratio at birth is biased towards females in a mongoose population. If the probability of having a daughter is 0.7 in this population, and if sex determination of each offspring is an independent event, then the probability that a female with a litter of four offspring has at least one son is \(\underline{\hspace{0cm}}\) (Round off to two decimal places.)
Show Hint
To calculate the probability of having at least one son, subtract the probability of having no sons from 1. This technique is useful when dealing with complementary events.
Updated On: Dec 24, 2025
Show Solution
Verified By Collegedunia
Correct Answer: 0.74
Solution and Explanation
Step 1: Understand the problem setup.
The question gives the probability of having a daughter as \( P(\text{daughter}) = 0.7 \). This implies that the probability of having a son is:
\[
P(\text{son}) = 1 - 0.7 = 0.3.
\]
Step 2: Calculate the probability of having no sons.
The probability of having no sons (i.e., all four offspring are daughters) is:
\[
P(\text{no sons}) = (0.7)^4 = 0.2401.
\]
Step 3: Calculate the probability of having at least one son.
The probability of having at least one son is the complement of the probability of having no sons:
\[
P(\text{at least one son}) = 1 - P(\text{no sons}) = 1 - 0.2401 = 0.7599.
\]
Step 4: Conclusion.
Thus, the probability that a female with four offspring has at least one son is approximately \( 0.76 \).
Was this answer helpful?
0
0
Top GATE EY Mathematics and Quantitative Ecology Questions
- All else being equal, which one of the following population sizes (𝑁) and migration rates (𝑚) would result in the most genetic differentiation between populations (𝐹𝑠𝑡)? Note that 𝐹𝑠𝑡 is computed as 𝐹𝑠t=1/4𝑁𝑚+1
- The Shannon-Weaver index 𝐻 is a measure of diversity and is calculated as H= -∑𝑝𝑖 𝑙𝑛(𝑝𝑖) where S is the total number of species and 𝑝𝑖 is the proportional abundance of a species i.The table below gives the abundance of different species in a community. The Shannon-Weaver index of reptile diversity in this community is ___________.(Rounded off to two decimal places)Species Abundance Indian gliding lizard 270 Malabar flying frog 325 Travancore tortoise 180 Malabar hornbill 160 Forest cane turtle 120 Malabar pit viper 30
- A researcher estimates the relationship between reproductive success (𝑁, number of offspring) and horn length (𝐻, in cm) in a wild goat as 𝑁 = 40 − 2.2𝐻 + 0.04𝐻 2 Horn length typically varies from 10 cm to 50 cm in this species. Which one of the following graphs correctly represents this relationship?
- Certain plants and animals rely on toxins such as cardiac glycosides for self-defense. Digitoxin and bufalin, structurally similar toxins produced by foxglove plants and bufonid toads, respectively, are one such example. Which one of the following statements about these toxins is correct?
- In a population of birds on an island, the average beak size reduced over one generation. A researcher estimated the association between beak size and relative fitness, shown in the graph. The estimated slope was \(-0.05\) with a 95% confidence interval of \(-0.15\) to \(0.09\).
View More Questions
Top GATE EY Probability Questions
Top GATE EY Questions
- If '\(\rightarrow\)' denotes increasing order of intensity, then the meaning of the words [\textit{simmer} \(\rightarrow\) \textit{seethe} \(\rightarrow\) \textit{smolder}] is analogous to [\textit{break} \(\rightarrow\) \textit{raze} \(\rightarrow\) \_\_\_\_\_\_]. Which one of the given options is appropriate to fill the blank?
- In a locality, the houses are numbered in the following way:The house-numbers on one side of a road are consecutive odd integers starting from \(301\), while the house-numbers on the other side of the road are consecutive even numbers starting from \(302\). The total number of houses is the same on both sides of the road. If the difference of the sum of the house-numbers between the two sides of the road is \(27\), then the number of houses on each side of the road is:
- For positive integers \( p \) and \( q \), with \( \frac{p}{q} \neq 1 \), \( \left( \frac{p}{q} \right)^q = p^{q-1 \). Then, which of the following is true?}
- Which one of the given options is a possible value of \(x\) in the following sequence? 3, 7, 15, x, 63, 127, 255
- On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?
View More Questions