You roll a six-sided die. Find the probability of each of the following scenarios. (a) Rolling a 5 or a number greater than 3. (b) Rolling a number less than 5 or an even number. (c) Rolling a 6 or an odd number.

Solution:

On rolling a die, the sample space = {1,2,3,4,5,6}

(a)The probability of rolling a 5 or a number greater than 3 is mathematically stated as:

P(rolling a or rolling a number greater than 3) = P(rolling a 5) + P(rolling a 4) + P(rolling a 5) + P(rolling a 6)

P(rolling a number 5) is getting repeated, hence the repetition has to be removed.

Therefore,

P(rolling a or rolling a number greater than 3) = P(rolling a 4) +P( rolling a 5) + P(rolling a 6)   = 1/6 + 1/6 + 1/6 = 3/6 = 1/2

P(>3) = 1/2

(b) P(rolling a number less than 5 or an even number) =P(rolling number 1) + P(rolling number 2) + P(rolling number 3) + P(rolling number 4) + P(rolling number 6)

= 1/6 + 1/6 + 1/6 +1/6 + 1/6 = 5/6

P(< 5 or an even number) = 5/6

(c) P(rolling a six or an odd number) = P(rolling number 1) + P(rolling number 3) + P(rolling number 5) + P(rolling number 6) = 1/6 + 1/6 + 1/6 + 1/6  = 4/6 = 2/3

P(=6 or odd number) = 2/3

You roll a six-sided die. Find the probability of each of the following scenarios. (a) Rolling a 5 or a number greater than 3. (b) Rolling a number less than 5 or an even number. (c) Rolling a 6 or an odd number.

Summary: 

On rolling dice the probability of  rolling a 5 or a number greater than 3 is 1/2  (b) Rolling a number less than 5 or an even number is 5/6 (c) Rolling a 6 or an odd number is 2/3