Question

Consider rolling a fair 8 sided die. The sample space is S = {1, 2, 3, 4, 5, 6, 7, 8} Find the following probabilities: Round to 3 decimal places. a. P(2) b. Plodd number) = c. P(not 7) = d. P(less than 6) = e. P(3.5) -

Answer 1

Solution :

Probability of an event E is given as follows :

P(E) = Number of favourable outcomes/Total number of outcomes

a) We have to find P(2)

P(2) = Number of 2's/Total number of outcomes

P(2) = 1/8

P(2) = 0.125

b) We have to find P(odd number).

P(odd number) = Number of odd numbers/Total number of outcomes

Number of odd numbers that we can get on rolling a 8 sided dice are 4. These odd numbers are 1, 3, 5 and 7.

Hence,

P(odd number) = 4/8

P(odd number) = 0.50

c) We have to find P(not 7).

P(not 7) = 1 - P(7)

P(7) = number of 7's/Total number of outcomes

P(7) = 1/8

Hence,

P(not 7) = 1 - (1/8)

P(not 7) = 7/8

P(not 7) = 0.875

d) We have to find P(less than 6).

P(less than 6) = Number of outcomes that are less than 6/Total number of outcomes

P(less than 6) = 5/8

P(less than 6) = 0.625

e) We have to find P(3.5).

P(3.5) = Number of 3.5's/Total number of outcome

Since, there are no outcome of 3.5 hence,

P(3.5) = 0/8

P(3.5) = 0

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