Question

Choose the pair of events that is mutually exclusive. (a). Even integers and multiples of 3 (b). Odd integers and multiples of 4 (c). Integers greater then 40 and integers less then 50. (d). Prime numbers and even integers

Answer 1

The answer is b. Multiples of 4 are never odd.
a) is wrong because 6 is both even and a multiple of 3
c) is wrong because all integers in the range 41..49 satisfy both events
d) is wrong because 2 is an even prime.

Answer 2

Answer:

(b). Odd integers and multiples of 4

Step-by-step explanation:

mutually exclusive  events are one or more events that does not occur simultaneously.

(a). Even integers and multiples of 3

Even numbers are 6, 12, 18... are also multiples of 3

Both even integers and multiples of 3 occur simultaneously so they are not mutually exclusive events.

(b). Odd integers and multiples of 4

multiples of 4 are 8,12,16, 20...... multiples of 4 cannot be an odd integer

So they are mutually exclusive events

(c). Integers greater then 40 and integers less then 50

41, 42, 43, 44, 45, 46, 47, 48, 49 are the integers that are greater than 40 and less than 50. So these integers satisfies both conditions

So they are not mutually exclusive events

(d). Prime numbers and even integers

2 is a prime number and also an integer

So they are not mutually exclusive events