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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 ​."

Respuesta :

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Answer:

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

Step-by-step explanation:

Given that:

For a coin toss :

Sample space = {HHTT, HTTT, THTT, TTTT, HHHT, HTHT, THHT, TTHT, HHTH, HTTH, THTH, TTTH, HHHH, 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." ​

{TTTT, HHHH}

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

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