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Sagot :
The probability of landing heads exactly 11 times when a coin is tossed 20 times is option a) 0.1602
The repeated tossing of a coin follows a binomial distribution
P(X = x) = ⁿCₓ pˣ (1 - p)⁽ⁿ ⁻ ˣ⁾
where,
n = No. of times the experiment was repeated
x = random variable defining the number of "successes"
p = probability of "success"
Here
"succeess" is the event of landing a head.
n = 20
x = no. of times heads should show, i.e 11
p = probability of landing a head in a single toss
= 1/2
Hence, putting all this in the formula above we get
P(X = 11) = ²⁰C₁₁ 0.5¹¹ (1 - 0.5)⁽²⁰ ⁻ ¹¹⁾
= ²⁰C₁₁ 0.5¹¹ 0.5⁹
= ²⁰C₁₁ 0.5²⁰
= 20!/ 11! (20 - 11)! X 0.5²⁰
= a) 0.1602
Complete Question
An unbiased coin is tossed 20 times.
Find the probability that the coin lands heads exactly 11 times
a. 0.1602
b. 0.5731
c. 0.2941
d. 0.1527
e. 0.6374
To learn more about probability visit
https://brainly.com/question/12844710
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