The document outlines the probability of drawing three specific cards from a standard deck of 52 cards without replacement. It calculates the probability for three conditions: the first card being a red ace, the second card being a 10 or jack, and the third card being greater than 3 but less than 7. The final calculated probability is approximately 0.00145.

1. Three cards are drawn in succession, without replacement, from an
ordinary deck of 52 cards, Find the probability that the first card is a
red ace, the second card is a 10 or Jack and the third card is greater
than 3 but less than 7.
Solution
There are 2 red Ace card in a deck, therefore
𝑷(𝑭𝒊𝒓𝒔𝒕 𝒄𝒂𝒓𝒅 𝒊𝒔 𝒂 𝒓𝒆𝒅 𝑨𝒄𝒆) = 𝑷(𝑨) =
𝟐
𝟓𝟐
There are 4 cards of 10 and 4 cards of Jack in a deck, second card
will be drawn from the remaining 51 cards. Therefore
𝑷(𝑺𝒆𝒄𝒐𝒏𝒅 𝒄𝒂𝒓𝒅 𝒊𝒔 𝒂 𝟏𝟎 𝒐𝒓 𝑱𝒂𝒄𝒌) = 𝑷(𝑩) =
𝟖
𝟓𝟏
There exists 12 card which are greaterthan 3 but less than 7, therefore
𝑷(𝑻𝒉𝒊𝒓𝒅 𝒄𝒂𝒓𝒅 𝒊𝒔 𝐠𝐫𝐞𝐚𝐭𝐞𝐫 𝐭𝐡𝐚𝐧 𝟑 𝐛𝐮𝐭 𝐥𝐞𝐬𝐬 𝐭𝐡𝐚𝐧 𝟕) = 𝑷(𝑪) =
𝟏𝟐
𝟓𝟎
Probability that three cards are drawn in succession, without replacement is
𝑷(𝑨 ∩ 𝑩 ∩ 𝑪) = 𝑷(𝑨) × 𝑷(𝑩
𝑨
⁄ ) × 𝑷(𝑪
𝑨 ∩ 𝑩
⁄ )
𝑷(𝑨 ∩ 𝑩 ∩ 𝑪) =
𝟐
𝟓𝟐
×
𝟖
𝟓𝟏
×
𝟏𝟐
𝟓𝟎
= 𝟎. 𝟎𝟎𝟏𝟒𝟓