Consider the following game: a drum contains 10 balls, each numbered from 1 to 10. three balls are randomly drawn, without replacement, from the drum. prior to the draw, you fill out a card by selecting three numbers from 1 to 10. to win a prize, the numbers you select have to correspond to the numbers of the balls drawn, in any order. what is the probability of winning a prize?

1/120

Step-by-step explanation: First to calculate the probability, we must know the possible number of way that 3 balls can be drawn from 10 balls numbered 1-10, and the number of ways that the 3 numbers selected from the player will match the number the numbers that the player chose.

To get the total number of outcomes this entails 10C3

From the formula nCr = n!/(r!(n-r)!)

10C3= 10!/(3!(10-3)!)

10! = 10*9*8*7*6*5*4*3*2*1 = 3628800

3! = 3*2*1 = 6

(10-3)! = 7! = 7*6*5*4*3*2*1 = 5040

10C3 = 3628800/(6*5040) = 120

Of all the 120 outcomes possible, only one outcome is expected to match all the 3 numbers that the player had written down, hence the probability for winning the draw will be

3C3/10C3

=1/120 = 0.0083333333333

∠EFA

Step-by-step explanation:

Linear pair : A linear pair is a pair of adjacent angles formed when two lines intersect and the sum of these angles is 180°

Vertical angles: The opposite angles formed by the two intersecting lines are called vertical angles.

Option 1) ∠BFC

Line BE and CF intersect at point F

So, the two adjacent angles formed when two lines intersect are ∠BFC and ∠EFC.

These are linear pair.

So,  ∠BFC is a part of linear pair.

Now by the definition of vertical angles , ∠BFC has no vertical pair.

So, ∠BFC is not a part of vertical pair.

Option 2) ∠CFG

According to the definition of linear pair ∠CFG is not a part of linear pair.

According to the definition of vertical pair ∠CFG is not a part of vertical pair.

Option 3) ∠GFD

According to the definition of linear pair ∠GFD has a linear pair ∠AFG

Thus ∠GFD is a part of linear pair

According to the definition of vertical pair ∠GFD is not a part of vertical pair.

Option 4) ∠EFA

According to the definition of linear pair ∠EFA has a linear pair ∠EFD

Thus ∠EFA is a part of linear pair

According to the definition of vertical pair ∠EFA has a ∠BFD vertical pair.

Thus ∠EFA is a part of vertical pair.

Hence ∠EFA is part of a linear pair and part of a vertical pair.

Click to let others know, how helpful is it