Question

SOMEONE PLZ ANSWER GIVING 45 POINTS FOR THIS QUESTION! A fair decimal die is tossed five times. Find the probability of obtaining an odd number of even digits.

Answer 1

Well, an even decimal die has probability 0.5 of rolling even and 0.5 of rolling odd.

The chances of rolling exactly one even number on five rolls is P(even)⋅(P(odd))4=0.5⋅0.54=0.55=132." role="presentation" style="margin: 0px; padding: 0px; outline: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">P(even)⋅(P(odd))4=0.5⋅0.54=0.55=132.P(even)⋅(P(odd))4=0.5⋅0.54=0.55=132.

The chances of rolling exactly three even numbers on five rolls is (P(even))3⋅(P(odd))2=0.53⋅0.52=0.55=132" role="presentation" style="margin: 0px; padding: 0px; outline: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">(P(even))3⋅(P(odd))2=0.53⋅0.52=0.55=132(P(even))3⋅(P(odd))2=0.53⋅0.52=0.55=132.

The chances of rolling exactly five even numbers on five rolls is (P(even))5=0.55=132" role="presentation" style="margin: 0px; padding: 0px; outline: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">(P(even))5=0.55=132(P(even))5=0.55=132.

Further, the probability of independent events is the sum of their probabilities, so the probability of rolling an odd number of even numbers is 332" role="presentation" style="margin: 0px; padding: 0px; outline: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">332