A coin is tossed 5 times. Find the probability that none are heads. Fi

Nefissi8u

Nefissi8u

Answered question

2021-11-17

A coin is tossed 5 times. Find the probability that none are heads. Find the probability that most 2 are heads, the probability that none are heads is?

Answer & Explanation

Maked1954

Maked1954

Beginner2021-11-18Added 17 answers

Step 1
When a coin is tossed there are 2 outcomes. Heads and tails.
So the probability of getting head is =p=12=0.5
Let us denote X= the number of heads
n= sample size =5
X follows a binomial distribution with n=5 and p=0.5
Step 2
The probability that none are heads is:
P(X=0)
=(5C0)(0.5)0(10.5)5
=0.03125.
The probability that at most 2 are heads is:
P(X2)
=P(X=0)+P(X=1)+P(X=2)
=(5C0)(0.5)0(10.5)5+(5C1)(0.5)1(10.5)4+(5C2)(0.5)2(10.5)3
=0.5
Answer: The probability that none are heads is =0.03125
The probability that at most 2 are heads is =0.5.

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