An honest coin is tossed 4 times in a row. Find the probability of each of the following events. (a) E1: "The coin comes up tails exactly twice." (b) E2: "All 4 tosses come up the same." (c) E3: "Exactly one-third of the tosses come up ." (d) E4: "The first 2 tosses come up heads ."

3/8 ; 1/8 ; 0 ; 1/4

Step-by-step explanation:

Given that:

For a coin toss :

Sample space = {HHTT, HTTT, THTT, , HHHT, HTHT, THHT, TTHT, HHTH, HTTH, THTH, TTTH, , HTHH, THHH, TTHH}

Probability = required outcome / Total possible outcomes

a) E1: "The coin comes up tails exactly twice."

p(E1) = 6/16 = 3/8

(b) E2: "All 4 tosses come up the same."

{, }

p(E2) = 2/16 = 1/8

(c) E3: "Exactly one-third of the tosses come up head."

1/3 of 4 ; p = 0 ; outcome is not a whole number

(d) E4: "The first 2 tosses come up heads ."

P(E4) = 4/16 = 1/4

45

step-by-step explanation: