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Arlecino [84]
3 years ago
7

A bag contains 4 white,5 blacks and 2 blue balls. 3 balls are drawn one after the other without replacement from the bag .what i

s the probability that they are of different color​
Mathematics
1 answer:
Doss [256]3 years ago
4 0

Answer:

24/99

Step-by-step explanation:

From the question given above, the following data were obtained:

White (W) balls = 4

Black (B) balls = 5

Blue (Bl) balls = 2

Probability that they are of different color =?

Next, we shall determine the total number of balls in the bag. This can be obtained as follow:

White (W) balls = 4

Black (B) balls = 5

Blue (Bl) balls = 2

TOTAL = 4 + 5 + 2 = 11 balls

Next, we shall determine the possible outcome of draw. This can be obtained as follow.

The possible outcome could be:

WBLB or WBBL or BBLW or BWBL or BLBW or BLWB

Next we shall determine the probability of each of outcomes.

Since the ball is drawn without replacement, it means the total number of ball will reduce after each draw.

White (W) balls = 4

Black (B) balls = 5

Blue (Bl) balls = 2

TOTAL = 11

P(WBLB) = 4/11 × 2/10 × 5/9 = 40/990

P(WBLB) = 4/99

P(WBBL) = 4/11 × 5/10 × 2/9 = 40/990

P(WBBL) = 4/99

P(BBLW) = 5/11 × 2/10 × 4/9 = 40/990

P(BBLW) = 4/99

P(BWBL) = 5/11 × 4/10 × 2/9 = 40/990

P(BWBL) = 4/99

P(BLBW) = 2/11 × 5/10 × 4/9 = 40/990

P(BLBW) = 4/99

P(BLWB) = 2/11 × 4/10 × 5/9 = 40/990

P(BLWB) = 4/99

Finally, we shall determine the probability that they are of different color. This can be obtained as follow:

P(WBLB) = 4/99

P(WBBL) = 4/99

P(BBLW) = 4/99

P(BWBL) = 4/99

P(BLBW) = 4/99

P(BLWB) = 4/99

Probability that they are of different color =?

Probability that they are of different color = P(WBLB) + P(WBBL) + P(BBLW) + P(BWBL) + P(BLBW) + P(BLWB)

= 4/99 + 4/99 + 4/99 + 4/99 + 4/99 + 4/99

= (4 + 4 + 4 + 4 + 4 + 4)/99

= 24/99

Thus, the probability that they are of different color is 24/99

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Answer:

\textsf{3.} \quad (x,y) \rightarrow (x-5,y+2)

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Step-by-step explanation:

<h3><u>Question 3</u></h3>

Given vertices of ΔLMN:

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Given vertices of ΔL'M'N':

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From inspection of the given diagram, we can see that the two triangles are congruent since their corresponding angles and corresponding side lengths are the same.  

There is no apparent reflection or rotation, so the transformation of ΔLMN to ΔL'M'N' is by translation.

To find the mapping rule for the translation, choose one pair of corresponding vertices and determine the difference between the x and y values of the translated point and the original point:

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y_{M'}-y_M =3-1=2 \implies \textsf{2 units up}

Therefore, the mapping rule for the translation is:

(x,y) \rightarrow (x-5,y+2)

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Given vertices of ΔLMN:

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Given vertices of ΔL'M'N':

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From inspection of the given diagram, we can see that the two triangles are congruent since their corresponding angles and corresponding side lengths are the same.  

There is no apparent reflection or rotation, so the transformation of ΔLMN to ΔL'M'N' is by translation.

To find the mapping rule for the translation, choose one pair of corresponding vertices and determine the difference between the x and y values of the translated point and the original point:

x_{L'}-x_L =-3-(-6)=3 \implies \textsf{3 units right}

y_{L'}-y_L =-3-(-4)=1 \implies \textsf{1 units up}

Therefore, the mapping rule for the translation is:

(x,y) \rightarrow (x+3,y+1)

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