Question

In a high school graduating class of 100 students , 54 studied mathematics , 69 studied history and 35 studied both mathematics & history , Find the probability that student took Mathematics or history ?

Answer 1

Answer:

100/123 is the answer for the question

Answer 2

Qᴜᴇsᴛɪᴏɴ:

• ɪɴ ᴀ ʜɪɢʜ sᴄʜᴏᴏʟ ɢʀᴀᴅᴜᴀᴛɪɴɢ ᴄʟᴀss ᴏғ 100 sᴛᴜᴅᴇɴᴛs, 54 sᴛᴜᴅɪᴇᴅ ᴍᴀᴛʜᴇᴍᴀᴛɪᴄs, 69 sᴛᴜᴅɪᴇᴅ ʜɪsᴛᴏʀʏ ᴀɴᴅ 35 sᴛᴜᴅɪᴇᴅ ʙᴏᴛʜ ᴍᴀᴛʜᴇᴍᴀᴛɪᴄs & ʜɪsᴛᴏʀʏ, ғɪɴᴅ ᴛʜᴇ ᴘʀᴏʙᴀʙɪʟɪᴛʏ ᴛʜᴀᴛ sᴛᴜᴅᴇɴᴛ ᴛᴏᴏᴋ ᴍᴀᴛʜᴇᴍᴀᴛɪᴄs ᴏʀ ʜɪsᴛᴏʀʏ?

Fɪɴᴅ:

• ᴛʜᴇ ᴘʀᴏʙᴀʙɪʟɪᴛʏ ᴛʜᴀᴛ sᴛᴜᴅᴇɴᴛ ᴛᴏᴏᴋ ᴍᴀᴛʜᴇᴍᴀᴛɪᴄs ᴏʀ ʜɪsᴛᴏʀʏ.

Sᴏʟᴜᴛɪᴏɴ:

• Number of students studied mathematics n (M) ➟ 54
• Number of students studied history n (H) ➟ 69
• Number of students studied history or mathematics both n (M U H) ➟ 35

★ ᴜsɪɴɢ ʀᴇʟᴀᴛɪᴏɴ:

➥ n (M U H) = n (M) + n (H) - n (M ∩ H)

➪ 54 + 69 - 35

➪ 123 - 35

➪ 88

• Let the event 'A' be " Student took mathematics or history ".

➝ Number of possible outcomes = Total no. of.

students = 100

➝ Number of favourable outcomes = 88

• Probability of event A = P (A) = No. of favourable outcomes / no. of possible outcomes.

➳ 88 / 100

➳ 22 / 25

• Therefore, the probability is 22 / 25 or 0.88.