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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!