In a family with 4 children,the probability t | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Total number of outcomes $= 2^4 = 16$. Let $X$ be the number of girls. We need to find the probability of at least two girls,i.e.,$P(X \ge 2)$. Th

Vedclass · Accepted Answer

$\frac{11}{16}$

Vedclass · Answer

(D) Total number of outcomes $= 2^4 = 16$. Let $X$ be the number of girls. We need to find the probability of at least two girls,i.e.,$P(X \ge 2)$. This can be calculated as $P(X \ge 2) = 1 - \{P(X=0) + P(X=1)\}$. For $P(X=0)$ (no girls,all boys): The only outcome is $\{BBBB\}$,so $P(X=0) = \frac{1}{16}$. For $P(X=1)$ (exactly one girl): The outcomes are $\{GBBB, BGBB, BBGB, BBBG\}$,so $P(X=1) = \frac{4}{16}$. Therefore,$P(X \ge 2) = 1 - \left(\frac{1}{16} + \frac{4}{16}\right) = 1 - \frac{5}{16} = \frac{11}{16}$.

In a family with $4$ children,the probability that there are at least two girls is:

Similar Questions

Ten eggs are drawn successively with replacement from a lot containing $10 \%$ defective eggs. Find the probability that there is at least one defective egg.

It is observed that $25\%$ of the cases related to child labour reported to the police station are solved. If $6$ new cases are reported,then the probability that at least $5$ of them will be solved is . . . . . .

The probability that an event will fail to happen is $0.05$. The probability that the event will take place on $4$ consecutive occasions is

In an experiment,a person gets success $\alpha$ times out of $\beta$ trials. If the experiment consists of $n$ trials,then the probability that he fails at least $(n-1)$ times is

Let $X \sim B(n, p)$ with mean $\mu$ and variance $\sigma^2$. If $\mu=2 \sigma^2$ and $\mu+\sigma^2=3$,then $P(X \leq 3)=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module