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Genrish500 [490]
3 years ago
14

The results of a survey in the cafeteria show that 20% of students like ketchup, 50% like mustard, and 15% like both ketchup and

mustard. What is the probability that a student likes neither ketchup nor mustard? A) 25% B) 45% C) 75% D) 85%
Mathematics
1 answer:
____ [38]3 years ago
5 0

Answer:

B) 45%

<em>The probability that neither K nor M occurs = P(K⁻∩M⁻) = 0.45 = 45%</em>

Step-by-step explanation:

<u><em>Explanation</em></u>:-

<em>Given data the results of a survey in the cafeteria show that 20% of students like ketchup.</em>

<em>Let "K" be the event of students like ketchup</em>

<em>P(K) = 20% = 0.20</em>

<em>Given data the results of a survey in the cafeteria show that  50% of students like mustard.</em>

<em>Let 'M' be the event of students like mustard</em>

<em>P(M) = 50% =0.50</em>

<em>Let 15% like both ketchup and mustard</em>

<em>P(K∩M) = 0.15</em>

<em>The probability that neither K nor M occurs = P(K⁻∩M⁻)</em>

<em>= P(S - (K∪M) </em>

<em>= P(S) - P(K∪M)</em>

<em>Total sample space P(S) =1</em>

<em>= 1 -  (P(K) +P(M) -P(K∩M)</em>

<em>= 1 - (0.20 + 0.50 - 0.15)</em>

<em>= 1 - 0.55 = 0.45</em>

<u><em>Final answer</em></u><em>:-</em>

<em>The probability that neither K nor M occurs = P(K⁻∩M⁻) = 0.45</em>

<em></em>

<em></em>

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