Question 10
A card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting neither a red card nor a queen.
Here, we will first find
Probability of getting either red card or queen
Now,
Number of red cards = 26
Number of queens = 4
But, out of these 4 queens, 2 are red
∴ Number of queens which are not red = 2
Now,
Number of cards which are red or queen = 26 + 2
= 28
P (getting either red card or queen)
= (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑑 𝑤ℎ𝑖𝑐ℎ 𝑎𝑟𝑒 𝑟𝑒𝑑 𝑜𝑟 𝑞𝑢𝑒𝑒𝑛)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑑𝑠)
= 28/52
= 7/13
Now,
P (not getting either red card or queen)
= 1 – P (getting either red card or queen)
= 1 – 7/13
= (13 − 7)/13
= 6/13
∴ Required probability is 𝟔/𝟏𝟑

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.