Question

A coin is tossed twice. let e e be the event "the first toss shows heads" and f f the event "the second toss shows heads". (a) are the events e e and f f independent? input yes or no here: yes (b) find the probability of showing heads on both toss. input your answer here: preview

Answer 1

Huh? couldn’t you retype

Answer 2

Answer:

a.Yes, Event E and F are independent.

b.$\frac{1}{4}$

Step-by-step explanation:

We are given that a coin is tossed twice.

S={HH,HT,TH,TT}

E={HH,HT}

F={HH,TH}

a.We have to find that event A and event B are independent or not.

We know that when two events A and B are independent then

$P(A)\cdot P(B)=P(A\cap B)$

Probability,P(E)=$\frac{number\;of\;favorable\;cases}{total\;number\;of cases}$

Total number of cases=4

P(E)=$\frac{2}{4}=\frac{1}{2}$

P(F)=$\frac{2}{4}=\frac{1}{2}$

$E\cap F$={HH}

$P(E\cap F)=\frac{1}{4}$

$P(E)\cdot P(F)=\frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}$

$\P(E)\cdot P(F)=P(E\cap F)$

Therefore, Event E and event B are  independent.

b.We have to find the probability of showing heads on both toss.

Number of favorable cases={HH}=1

Total number of cases=4

By using the formula of probability

The probability of getting heads on both toss=$\frac{1}{4}$