Consider the random experiment of tossing a fair coin five times,and let X denote the random variable that counts the number of times heads appears.Find $P ( X 3 )$
A) $\frac { 5 } { 16 }$
B) $\frac { 7 } { 8 }$
C) $\frac { 3 } { 16 }$
D) $\frac { 13 } { 16 }$

Question

Consider the random experiment of tossing a fair coin five times,and let X denote the random variable that counts the number of times heads appears.Find $P ( X > 3 )$
A) $\frac { 5 } { 16 }$
B) $\frac { 7 } { 8 }$
C) $\frac { 3 } { 16 }$
D) $\frac { 13 } { 16 }$

Quizplus · Accepted Answer

The probability $P(X > 3)$ means we are looking for the probability of getting more than 3 heads in 5 tosses, which includes getting 4 heads or 5 heads. The total number of outcomes is $2^5 = 32$. The number of ways to get exactly 4 heads is $5C4 = 5$, and the number of ways to get exactly 5 heads is $5C5 = 1$. So, the total favorable outcomes are $5 + 1 = 6$. Therefore, $P(X > 3) = \frac{6}{32} = \frac{3}{16}$.

Consider the Random Experiment of Tossing a Fair Coin Five P(X>3)P ( X > 3 )P(X>3)

Consider the Random Experiment of Tossing a Fair Coin Five $P ( X > 3 )$