Question

3. In the game of Bingo, a number is selected at random. If it is a number between 1 and 15, then the letter "B" has been chosen. If it is a number between 16 and 30, then the letter "T" has been chosen. Similarly, if it is a number between 31 and 45, 46 and 60, or 61 and 75, then the letters "N". "G", or "O" have been chosen, respectively. Find the probability that either a "G", an even number, or a multiple of 3 is selected as the first number in Bingo.

Answer 1

In the game of Bingo, a number is selected at random. If it is a number between 1 and 15, then the letter "B" has been chosen. If it is a number between 16 and 30 ,then the letter "I" has been chosen. Similarly, if it is a number between 31 and 45, 46 and 60, or 61 and 75, then the letter " N" , "G", or "O" have been chosen respectively, Find the probability that either a "G", an even number, or a multiple of 3 is selected as the first number in Bingo.

=> Solution :-

Given data -

• Let the event that "G' is chosen be denoted as Gt. • let the event that an even number is chosen be denoted as E. • let the event that a multiple of Q is chosen be denoted as M. o Required Probability = P (GUE UM) - PCC) + P(E) + PCM) - PCGPn E) - PCCO m) - PIENM) + P (GHOEOM) ecol- Number of numbers between 61 and 75 75 15 Gs Scanned with CamScanner

•PCE) = Number of even numbers between 1 and 75 75 of 3 • P (M) = Clumber of multiples between 1 and 75 75 - 25 to 25 • PCGNE) - Vumbers of even numbers between 67 and 75 75 Scanned with Cam Scanner 75

• PCG nM) = 3 between ol and 75 Clumber of multiples of 75 •PCEOM) = (vumber of even numbers of 3 between 1 and 75 75 - 2 •PCGOEOM) = Number of even number multiples of 3 between 61 and 75 75 cs Scanned with Scanned with CamScanner = a

:. Required Probability = = P(61) + P(E) + P(M) - P(640E) - - P(GAM) - P(GNEAM) + + - 55 75 = 11 ICS Scanned 115 EartscaTTITET